Increasing numbers of Americans believe that the White House (against evidence to the contrary) directed the IRS to target conservative groups—and a majority even wants a special prosecutor to get to the bottom of the matter. But Ronald Reagan would have said that in such a huge pile of dung there has to be a pony somewhere, and in this case, that pony is tax reform. When Americans are brimming with resentment at the IRS, why not seize the moment to overhaul the bloated, incomprehensible, unfair tax code?

Granted, tackling personal income taxes is probably unrealistic so soon after the fiscal-cliff deal raising rates for the wealthy. But when it comes to corporate taxes, there’s a real opportunity, since Barack Obama and other Democrats are willing to accept revenue-neutral reforms (a requirement for Republicans). Here’s what the president should call for:

1 Lower the rates, close the loopholes

Right now, corporations are taxed at 35 percent. That rate is high compared with other developed nations and—not coincidentally—routinely dodged thanks to dedicated accountants and the proliferation of business- friendly breaks. Any reform would seek to lower the rate and recover the revenue by closing dozens of loopholes. Obama wants a corporate rate of 28 percent and key Republicans have suggested 25 percent—a bridgeable gap. Incentives that could be reduced or eliminated include the domestic production deduction, an effort to keep manufacturing operations stateside that is defined so broadly that burger joints qualify. Then there are a host of notorious industry-specific breaks, like oil-and-gas subsidies and the carried-interest loophole, which taxes private-equity managers at half the rate of other high earners.

Illustration by Zohar Lazar

Several dozen giants—including Walmart, Google, and GE—say they support a more efficient code, even if it penalizes them. The tougher obstacle will be businesses organized as limited liability companies and so-called “S corporations,” which pass all gains to owners or shareholders, respectively. Since such entities don’t pay corporate taxes, they won’t benefit from the rate drop but will get hit by the cuts in credits. They’ll cast themselves as struggling mom-and-pops, although many are anything but—unless you count Bain Capital as a mom-and-pop concern.

2 No more tax havens

In theory, the IRS taxes the worldwide income of U.S.-based companies, while granting credits to offset the taxes those companies pay abroad. In practice, the United States allows corporations to defer declaring their offshore profits indefinitely. Along with other loopholes, this means U.S. multinationals effectively get to decide how much tax they feel like paying.

Many multinationals want the United States to adopt the system used by other developed nations, under which taxes are owed to the countries where income is earned. Alone, this arrangement would encourage considerable gaming, since corporations would establish operations in low-tax countries. But there are hybrid models to guard against abuse. The government could curb the most brazen havens by setting a minimum tax for income claimed abroad. It could also require more disclosure of what corporations earn and pay. As Kim Clausing, an international tax expert at Reed College, noted, “The firms would have a hard time arguing against it themselves in the light of day.”

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3 Simplify the code

The administration could do a lot of good just by making large sections of the tax code comprehensible to mere mortals. There are 20 tax-favored savings vehicles—including 401(k)s, IRAs, health savings accounts, and college-savings plans—which could be reduced to a handful. Calculating capital gains taxes on many investments is an accountant’s dream, because only a professional could possibly figure it out. These things might not affect the average person’s 1040, but anything that makes the domain of IRS bureaucrats less inscrutable can only play well right now.

... And Pray This Guy Helps You

To liberals, Max Baucus has long been a reliable villain—a powerful Democrat who undermines Democratic aims. As chairman of the Senate Finance Committee, Baucus cut the deal that enabled the first of President George W. Bush’s massive tax cuts for the rich. During the debate over the Affordable Care Act, his mostly futile negotiations with Republicans nearly sank the entire effort. He was one of the crucial votes that led to the defeat of the post-Newtown gun-control bill, even though he’s retiring from Congress in 2014.

But now Baucus has a chance at redemption. With an eye on his legacy, he has teamed up with Republican House Ways and Means Committee Chairman Dave Camp (who is also keen to make his mark before stepping down from his position next year), and the duo has been crafting proposals for sweeping tax reform. Previously, Baucus’s record on this front hasn’t been stellar: It’s no accident that at least 28 of his former staffers have gone to work as tax lobbyists; many of the loopholes he is trying to fix appeared on his watch. But now he seems genuinely eager to leave a fairer and cleaner tax code behind him. President Obama should give him all the help he can.